Two adjacent sides of a rectangle are
$6 x^{2} + 4 y^{2} + 2 x y a n d x^{2} - 2 x + 4 x y$ .
Find its perimeter?

7 x^{2} + 6 x y + 4 y^{2} - 2 x

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14 x^{2} + 12 x y + 8 y^{2} - 4 x

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7 x^{2} + 6 x y + 8 y^{2} - 4 x

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14 x^{2} + 12 x y + 4 y^{2} - 2 x

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Solution

The correct option is B $14 x^{2} + 12 x y + 8 y^{2} - 4 x$
Given the adjacent sides of the rectangle are
$6 x^{2} + 4 y^{2} + 2 x y a n d x^{2} - 2 x + 4 x y$
The perimeter of the rectangle = 2(length + breadth)
So, the perimeter
$= 2 [(6 x^{2} + 4 y^{2} + 2 x y) + (x^{2} - 2 x + 4 x y)]$
$= 2 (7 x^{2} + 6 x y + 4 y^{2} - 2 x$ )
$= 14 x^{2} + 12 x y + 8 y^{2} - 4 x$
Hence, the perimeter of the rectangle
$= 14 x^{2} + 12 x y + 8 y^{2} - 4 x$

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